GATE ME 2026 Set 1 — Question 39
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Engineering Mathematics → Probability → Axioms of Probability
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Question
A student council of 10 members consists of two students from engineering school, three students from science school and five students from arts school. The university administration selects three students from the council at random. What is the chance that out of the selected students, two belong to the same school and the third belongs to different school?
Correct answer
(A) 79/120
Solution
Total number of ways to select 3 students from 10 is .
We need to find the number of ways to select 2 students from one school and 1 student from a different school.
Case 1: 2 from Engineering (2 available) and 1 from others (8 available).
Ways = .
Case 2: 2 from Science (3 available) and 1 from others (7 available).
Ways = .
Case 3: 2 from Arts (5 available) and 1 from others (5 available).
Ways = .
Total favorable ways = .
Probability = .
We need to find the number of ways to select 2 students from one school and 1 student from a different school.
Case 1: 2 from Engineering (2 available) and 1 from others (8 available).
Ways = .
Case 2: 2 from Science (3 available) and 1 from others (7 available).
Ways = .
Case 3: 2 from Arts (5 available) and 1 from others (5 available).
Ways = .
Total favorable ways = .
Probability = .
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